Nonisothermal CSTR model

Example 9Ji. The nonisothermal CSTR modeled in Sec. 3.6 can be linearized (sec Prob. 6.12) to give two linear ODEs in teinis of perturbation variables. 

The steady state model for a nonisothermal CSTR representing a catalytic converter is ... 

Kahlert et al. (1981) proposed a simplified model for nonisothermic CSTR reaction exhibiting horatian oscillations. 

Substituting the approximation above into eqs. (6.28) and (6.29), we take the following linearized model for a nonisothermal CSTR ... 

V.20 In Example 6.4 we developed the linearized model of a nonisothermal CSTR. Develop a nonlinear steady-state feedforward controller which maintains the value of c A at the desired set point in the presence of changes in cAp Tt. The coolant temperature Tc is the manipulated variable. 

A model of a nonisothermal CSTR in which an irreversible first-order reaction, A—> B, takes place can be formulated as follows (Frank-Kamenetskii, 1969 Bykov and Tsybenova, 2011) ... 

The sum of squares as defined by Equation 7.8 is the general form for the objective function in nonlinear regression. Measurements are made. Models are postulated. Optimization techniques are used to adjust the model parameters so that the sum-of-squares is minimized. There is no requirement that the model represent a simple reactor such as a CSTR or isothermal PER. If necessary, the model could represent a nonisothermal PFR with variable physical properties. It could be one of the distributed parameter models in Chapters 8 or 9. The model... 

The solution of the nonlinear optimization problem (PIO) gives us a lower bound on the objective function for the flowsheet. However, the cross-flow model may not be sufficient for the network, and we need to check for reactor extensions that improve our objective function beyond those available from the cross-flow reactor. We have already considered nonisothermal systems in the previous section. However, for simultaneous reactor energy synthesis, the dimensionality of the problem increases with each iteration of the algorithm in Fig. 8 because the heat effects in the reactor affect the heat integration of the process streams. Here, we check for CSTR extensions from the convex hull of the cross-flow reactor model, in much the same spirit as the illustration in Fig. 5, except that all the flowsheet constraints are included in each iteration. A CSTR extension to the convex hull of the cross-flow reactor constitutes the addition of the following terms to (PIO) in order to maximize (2) instead of [Pg.279]

The influence of activity changes on the dynamic behavior of nonisothermal pseudohomogeneoiis CSTR and axial dispersion tubular reactor (ADTR) with first order catalytic reaction and reversible deactivation due to adsorption and desorption of a poison or inert compound is considered. The mathematical models of these systems are described by systems of differential equations with a small time parameter. Thereforej the singular perturbation methods is used to study several features of their behavior. Its limitations are discussed and other, more general methods are developed. 

Use of the CSTR sequence as a model for nonideal reactors has been criticized on the basis that it lacks certain aspects of physical reality, such as the absence of backward communication between the individual mixing cell units. Such may be the case nonetheless the mathematical simplicity of the approach makes it very attractive, particularly for systems with complex kinetics, nonisothermal effects, or other complicating factors. 

The difficulty in this is the awkward form of equation (6-140) with respect to 7). One likes to compute in sequence through the series of cells, but here we face the implicit form of Ti as a function of r, i. This is the same basic difficulty that limits the utility of the CSTR sequence as an analytical model for nonisothermal reactors. For the case here though, where we employ a relatively large value of the index n in approximation of a plug-flow reactor, and where the solution will be via numerical methods anyway, we will strong-arm the problem with the approximation T,- r,- ] in the exponentials, so that... 

The most important feature of a CSTR is its mixing characteristics. The idealized model of reactor performance presumes that the reactor contents are perfectly mixed so that the properties of the reacting fluid are uniform throughout. The composition and temperature of the effluent are thus identical with those of the reactor contents. This feature greatly simplifies the analysis of stirred-tank reactors vis-h-vis tubular reactors for both isothermal and nonisothermal... 

The authors of [104] attempted a qualitative and even semiquantitative analysis of the thermokinetic interactions and the nonlinear nature of this highly exothermic system. The results obtained from nonisothermal modeling of the process are qualitatively consistent with the above experimental results. A detailed mathematical description of the kinetics and processes of heat and heat transfer in a CSTR made it possible to reproduce the appearance of temperature hysteresis and to demonstrate its dependence on the oxygen concentration, reaction time, and temperature of the reactor walls. Figure 8.6 shows the calculated self-heating... 

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